What should be added to the polynomial $x^{2} - 5 x + 4,$ so that (x - 3) is factor of the resulting polynomial?

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Solution

Let $f (x) = x^{2} - 5 x + 4$
substituting x = 3.
$f (x) = 3^{2} - 5 (3) + 4$
= 9 - 15 + 4
= 13 - 15
= -2.
$∴$ 2 must be added to f(X) such that (x-3) is a factor of
f(x) .

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